Calculate the acceleration of the block $B$ in the shown figure, assuming the surfaces and the pulleys $p_1$ and $p_2$ are smooth and the string is light.

The correct option is A $\frac{3F}{17m}m/s^2$
Let the acceleration of block $A$ is $a$ and block $B$ is $b$
From Constrained condition and using intercept method we have,
${\stackrel{..}{L}}_1+{\stackrel{..}{L}}_2+{\stackrel{..}{L}}_3=0$
$\Rightarrow -b+a+a-b-b+0=0$
$\Rightarrow 2a=3b$ ...(1)





From the FBDs of the blocks we have
$F-2T=2ma=2m\left(\frac{3b}{2}\right)=3mb$
Or, $T=\frac{F-3mb}{2}$ ...(2)
$3T=4mb\Rightarrow T=\frac{4mb}{3}...\left(3\right)$
On solving (2) & (3) we get
$b=\frac{3F}{17m}$
Thus, the acceleration of the block $B$ is $b=\frac{3F}{17m}$